Finite Group Databasebeta

← #25063877

Subgroups — #25063877

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2#19136978C211yesmaximal, characteristic, complemented
3#19133139C214yesmaximal, complemented
4#19133129C212yesmaximal, complemented
5#19133125C212yesmaximal, complemented
6#19133087C214yesmaximal, complemented
7C2×C43×#407C211yesmaximal, characteristic, complemented
8C22×#10621898C411yescharacteristic, complemented
9#14583410—21no—
10#14583410—21no—
11#14583410—21no—
12#14583410—21no—
13#14583410C412yescomplemented
14#14583410C412yescomplemented
15#14583410C2212yes—
16#14583410C2212yes—
17C2×#13063308—21no—
18C2×#13063304C411yescharacteristic, complemented
19C2×#13063304C2211yescharacteristic
20C2×#13063299C411yescharacteristic, complemented
21C2×#13063299C2211yescharacteristic
22C2×#13063294—21no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284—21no—
26C2×#13063284C411yescharacteristic, complemented
27#14582762C2212yes—
28#14582759—21no—
29#14582759C2212yescomplemented
30#14582755—21no—
31C4×C22⋊Dic43—21no—
32C4×C22⋊Dic43C2212yescomplemented
33#14582637C2218yescomplemented
34#14582634C2218yescomplemented
35C24×C4×C43C2211yescharacteristic
36C22×M16×C43—21no—
37C43×#407—21no—
38C43×#407—21no—
39C43×#407C2212yes—
40C43×#407C2212yescomplemented
41C2×C22⋊C8×C43—21no—
42C2×C22⋊C8×C43C2212yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—44no—
46C2×#10621898C2×C412yes—
47C2×#10621898C2×C412yes—
48C22×Dic86C2×C411yescharacteristic
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C4×D43—21no—
54#13063308—22no—
55#13063308—22no—
56#13063308—22no—
57#13063308—22no—
58#13063304—21no—
59#13063304—21no—
60#13063304—21no—
61#13063304—21no—
62#13063304C2×C412yes—
63#13063304C2×C412yes—
64#13063304C2×C412yes—
65#13063304C2312yes—
66#13063299—21no—
67#13063299—21no—
68#13063299—21no—
69#13063299—21no—
70#13063299C2×C412yes—
71#13063299C2×C412yes—
72#13063299C2×C412yes—
73#13063299C2312yes—
74#13063294—22no—
75#13063294—22no—
76#13063294—22no—
77#13063294—22no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86#13063284—21no—
87#13063284—21no—
88#13063284—44no—
89#13063284C2×C412yes—
90#13063284C2×C412yes—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C43⋊#95—22no—
107C43⋊#95C2314yes—
108C25×C43D411yescharacteristic
109C23×C4×C43—44no—
110C23×C4×C43C2×C411yescharacteristic
111C23×C4×C43C2×C411yescharacteristic
112C23×C4×C43C2×C411yescharacteristic
113C23×C4×C43C2×C411yescharacteristic
114C23×C4×C43D411yescharacteristic
115C23×C4×C43D411yescharacteristic
116C23×C4×C43D411yescharacteristic
117C23×C4×C43D411yescharacteristic
118C23×C4×C43D411yescharacteristic
119C23×C4×C43D411yescharacteristic
120C23×C4×C43D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—44no—
127C22×C8×C43—22no—
128C22⋊C8×C43—22no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C22⋊C8×C43C2314yes—
132C24×C43—42no—
133C24×C43—42no—
134C24×C43—42no—
135C24×C43C22⋊C411yescharacteristic
136C24×C43C22⋊C411yescharacteristic
137C24×C43C22⋊C411yescharacteristic
138C24×C43C22⋊C411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43C22⋊C411yescharacteristic
158C22×C4×C43C22⋊C411yescharacteristic
159C22×C4×C43C22⋊C411yescharacteristic
160C22×C4×C43C22⋊C411yescharacteristic
161C22×C4×C43C22⋊C411yescharacteristic
162C22×C4×C43C22⋊C411yescharacteristic
163C22×C4×C43C22⋊C411yescharacteristic
164C22×C4×C43C22⋊C411yescharacteristic
165C22×C4×C43C22⋊C411yescharacteristic
166C22×C4×C43C22⋊C411yescharacteristic
167C22×C4×C43C22⋊C411yescharacteristic
168C22×C4×C43C22⋊C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—44no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—24no—
198#10621898—44no—
199#10621898—44no—
200#10621898—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—42no—
204C2×D172C22×C412yes—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—44no—
208C2×Dic86—21no—
209C2×Dic86—42no—
210C2×Dic86C22×C412yes—
211M16×C43—44no—
212M16×C43—44no—
213C2×C8×C43—24no—
214C2×C8×C43—44no—
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217C22⋊Dic43—22no—
218C22⋊Dic43—22no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—44no—
222C22⋊Dic43—44no—
223C22⋊Dic43—44no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—44no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C22×C412yes—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237C4×Dic43—22no—
238C4×Dic43—22no—
239C4×Dic43—44no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—416no—
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C22×D411yescharacteristic
269C22×D43—22no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43#9914yes—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C22⋊D43—44no—
310C22⋊D43—44no—
311C22⋊D43—44no—
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—44no—
322C2×Dic43—44no—
323C2×Dic43—44no—
324D172—42no—
325D172—42no—
326C4×D43—44no—
327C4×D43—44no—
328Dic86—42no—
329Dic86—42no—
330C8×C43—44no—
331#17559—431nomaximal, Sylow
332C22×C43—21no—
333C22×C43—21no—
334C22×C43—21no—
335C22×C43—21no—
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—44no—
351C22×C43—44no—
352C22×C43—44no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43—44no—
357C22×C43C2×#9912yes—
358C22×C43#42112yes—
359C22×C43C22×C22⋊C411yescharacteristic
360C22×C43#57512yes—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—84no—
365C4×C43—21no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43C2×#9912yes—
372C4×C43C2×#9912yes—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—84no—
377C2×#525—431no—
378C2×#407D4311yescharacteristic, complemented
379#2280—431no—
380#1513—434no—
381#1511—432no—
382#1510—432no—
383#1501—434no—
384C2×C43—22no—
385C2×C43—22no—
386C2×C43—22no—
387C2×C43—41no—
388C2×C43—41no—
389C2×C43—41no—
390C2×C43—41no—
391C2×C43C22×#9911yescharacteristic
392C2×C43#289611yescharacteristic
393C2×C43C2×#42111yescharacteristic
394D43—82no—
395C22×#41—431no—
396C24×C4C2×D4311yescharacteristic
397C22×M16—21no—
398#525—432no—
399#525—432no—
400#525—432no—
401#525—432no—
402#525—861no—
403#525—861no—
404#525—861no—
405#525—861no—
406C2×#123—861no—
407C2×C22⋊Q8—431no—
408C2×C22⋊Q8—431no—
409C2×#121—431no—
410C2×#121—431no—
411C2×#120—861no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×#117—431no—
415C2×#117—861no—
416#407—21no—
417#407—21no—
418#407C2×D4312yes—
419#407C2×D4312yescomplemented
420C2×C22⋊C8—21no—
421C2×C22⋊C8C2×D4312yescomplemented
422#381—432no—
423#380—432no—
424#380—861no—
425#379—861no—
426C4×C22⋊C4—432no—
427C4×C22⋊C4—861no—
428#328—438no—
429#327—438no—
430C43#1755911yescharacteristic, complemented, Sylow
431C25D17211yescharacteristic
432C2×#41—432no—
433C2×#41—432no—
434C2×#41—861no—
435C2×#41—861no—
436C2×#41—1724no—
437C22×Q8—431no—
438C22×D4—431no—
439C22×D4—861no—
440C22×D4—861no—
441C22×D4—861no—
442C23×C4—44no—
443C23×C4—861no—
444C23×C4C4×D4311yescharacteristic
445C23×C4C4×D4311yescharacteristic
446C23×C4C4×D4311yescharacteristic
447C23×C4C4×D4311yescharacteristic
448C23×C4D17211yescharacteristic
449C23×C4D17211yescharacteristic
450C23×C4D17211yescharacteristic
451C23×C4C22⋊D4311yescharacteristic
452C23×C4C22⋊D4311yescharacteristic
453C23×C4C22⋊D4311yescharacteristic
454C23×C4C22⋊D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456C23×C4C22×D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—44no—
461C22×C8—22no—
462#123—862no—
463#123—862no—
464#123—862no—
465#123—862no—
466C22⋊Q8—432no—
467C22⋊Q8—432no—
468C22⋊Q8—432no—
469C22⋊Q8—432no—
470C22⋊Q8—861no—
471C22⋊Q8—861no—
472C22⋊Q8—861no—
473C22⋊Q8—861no—
474#121—432no—
475#121—432no—
476#121—432no—
477#121—432no—
478#121—861no—
479#121—861no—
480#121—861no—
481#121—861no—
482#120—862no—
483#120—862no—
484#120—862no—
485#120—862no—
486C4×D4—862no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494#117—432no—
495#117—432no—
496#117—861no—
497#117—861no—
498#117—1724no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—862no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C42—861no—
513C2×C42—862no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C22×D4314yes—
518#95—434no—
519#95—862no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—861no—
524C24(C2×D43)⋊C411yescharacteristic
525C24(C2×D43)⋊C411yescharacteristic
526C24(C2×D43)⋊C411yescharacteristic
527C24(C2×D43)⋊C411yescharacteristic
528C24C2×D17211yescharacteristic
529C24C2×D17211yescharacteristic
530C24C2×D17211yescharacteristic
531#41—1724no—
532#41—1724no—
533#41—1724no—
534#41—1724no—
535C2×Q8—432no—
536C2×Q8—861no—
537C2×Q8—1722no—
538C2×D4—432no—
539C2×D4—862no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—861no—
546C2×D4—1722no—
547C2×D4—1724no—
548C2×D4—1724no—
549C2×D4—1724no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—864no—
570C22×C4—1724no—
571C22×C4(C2×D43)⋊C411yescharacteristic
572C22×C4(C2×D43)⋊C411yescharacteristic
573C22×C4(C2×D43)⋊C411yescharacteristic
574C22×C4(C2×D43)⋊C411yescharacteristic
575C22×C4(C2×D43)⋊C411yescharacteristic
576C22×C4(C2×D43)⋊C411yescharacteristic
577C22×C4(C2×D43)⋊C411yescharacteristic
578C22×C4(C2×D43)⋊C411yescharacteristic
579C22×C4(C2×D43)⋊C411yescharacteristic
580C22×C4(C2×D43)⋊C411yescharacteristic
581C22×C4(C2×D43)⋊C411yescharacteristic
582C22×C4(C2×D43)⋊C411yescharacteristic
583C22×C4C2×C4×D4311yescharacteristic
584C22×C4C2×C4×D4311yescharacteristic
585C22×C4C2×C4×D4311yescharacteristic
586C22×C4C2×C4×D4311yescharacteristic
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C2×D17211yescharacteristic
590C22×C4C2×D17211yescharacteristic
591C22×C4C2×D17211yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C23×D4311yescharacteristic
599M16—44no—
600M16—44no—
601C2×C8—24no—
602C2×C8—44no—
603C4⋊C4—432no—
604C4⋊C4—432no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—862no—
608C4⋊C4—862no—
609C4⋊C4—862no—
610C4⋊C4—862no—
611C4⋊C4—1724no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—1724no—
623C22⋊C4—1724no—
624C22⋊C4—1724no—
625C42—862no—
626C42—862no—
627C42—1724no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—862no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23C2×(C2×D43)⋊C411yescharacteristic
655C23C2×(C2×D43)⋊C411yescharacteristic
656C23C2×(C2×D43)⋊C411yescharacteristic
657C23C2×(C2×D43)⋊C411yescharacteristic
658C23C2×(C2×D43)⋊C411yescharacteristic
659C23C2×(C2×D43)⋊C411yescharacteristic
660C23C22×D17211yescharacteristic
661Q8—1722no—
662Q8—1722no—
663D4—1722no—
664D4—1722no—
665D4—1724no—
666D4—1724no—
667D4—1724no—
668D4—1724no—
669D4—1724no—
670D4—1724no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—1724no—
702C2×C4—1724no—
703C2×C4—1724no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1724no—
708C2×C4—1724no—
709C2×C4#1306323914yes—
710C2×C4C2×(C2×D43)⋊C411yescharacteristic
711C2×C4C2×(C2×D43)⋊C411yescharacteristic
712C2×C4C2×(C2×D43)⋊C411yescharacteristic
713C2×C4C2×(C2×D43)⋊C411yescharacteristic
714C2×C4C2×(C2×D43)⋊C411yescharacteristic
715C2×C4C2×(C2×D43)⋊C411yescharacteristic
716C2×C4C22×C4×D4311yescharacteristic
717C2×C4C22×C22⋊D4311yescharacteristic
718C8—44no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—3444no—
745C22—1722no—
746C22—1722no—
747C22—1722no—
748C22C2×#1306323912yes—
749C22#1458291512yes—
750C22C22×(C2×D43)⋊C411yescharacteristic
751C22#1458369912yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—3444no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4C2×#1306323912yes—
763C4C2×#1306323912yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—3442no—
772C2C22×#1306323911yescharacteristic
773C2#1914311511yescharacteristic
774C2C2×#1458291511yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43#17559
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19136978C2semidirect
3. #19133139C2semidirect
4. #19133129C2semidirect
5. #19133125C2semidirect
6. #19133087C2semidirect
7. C2×C43×#407C2semidirect
8. C22×#10621898C4semidirect
13. #14583410C4semidirect
14. #14583410C4semidirect
18. C2×#13063304C4semidirect
20. C2×#13063299C4semidirect
26. C2×#13063284C4semidirect
29. #14582759C22semidirect
32. C4×C22⋊Dic43C22semidirect
33. #14582637C22semidirect
34. #14582634C22semidirect
40. C43×#407C22semidirect
42. C2×C22⋊C8×C43C22semidirect
378. C2×#407D43semidirect
419. #407C2×D43semidirect
421. C2×C22⋊C8C2×D43semidirect
430. C43#17559semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834102
#191369782
#191331392
#191331292
#191331252
#191330872
C2×C43×#4072
#1755943